Page 101 - ITU Journal, Future and evolving technologies - Volume 1 (2020), Issue 1, Inaugural issue

ITU Journal on Future and Evolving Technologies, Volume 1 (2020), Issue 1

RIM
becomes

( , Φ) = ∑ ∑ / ( , Φ )⋅

V2I =1 =1 (2)
RIM RSU
I2V Γ /Φ ( , Φ) 0 ( ,Φ) ,
V2V V2V
where and are the amplitude and phase of the
wave incident to the ( , )-th unit cell, respectively, with
= [1, 2, … , ] and = [1, 2, … , ]. In Eq. (2), Γ
Fig. 1 – Vehicular communications paradigm based on the use of and Φ are the amplitude and phase of the response of
RIMs as relay node, for data transmission to a receiver node (green the ( , )-th unit cell, respectively; ( , ) denotes the
vehicle), in case of Vehicle-to-Vehicle (black lines) and Vehicle-to- scattering diagram of the ( , )-th unit cell towards an
Infrastructure/Infrastructure-to-Vehicle (blue lines).
arbitrary direction of reflection, whereas ( , Φ ) de-

notes the response of the ( , )-th unit cell at the direc-
tion of incidence determined by , Φ and = 2 / is

0

0
the wave number. Finally, we introduce ( , Φ), which
denotes the relative phase shift of the unit cells with re-
spect to the radiation pattern coordinates, given by
1 1
( , Φ) = ( ) [( − ) (Φ) + ( − ) (Φ)] ,

2 2
(3)
(a) with [m] as the unit cell size.

In order to make the model able to be calculated, we make
a further assumption in the point of plane incident wave
view, so that factors , , and ( , Φ ) are con-

stants for all and indexes. In addition, we apply the
widespread assumption to the scattering pattern of the
unit cell, which is modeled over the positive semisphere
with the function ( ), which is a widespread assump-
tion, [11]. Finally, and without loss of generality, we con-
sider the normal incidence i.e., ( = Φ = 0). Then,

(b) Eq. (2) becomes [11]

Fig. 2 – (a) The configuration and the geometry of the proposed unit
0
cell with a U-shaped radiating patch, and (b) unit cells with PIN diode’s ( , Φ) = ( ) ∑ ∑ Γ [Φ + ( , Φ)],
equivalent circuit model for ON and OFF states. =1 =1
(4)
ered as a particular case of wavefront manipulation that with as a constant.
occurs in the far field. Regarding the Huygens princi-
In order to have anomalous reflection, the main objective
ple, the meta-surface structures can be considered as an is controlling the phase shift of the unit cells Φ
integrated EM radiator array [20]. Herein, in order to . In par-
ticular, we manipulate the phase of the reflected wave-
model the meta-antenna array, we consider a method that
form but not its amplitude. In this current version we do
has been validated in several works via extensive simula-
not focus on the control scheme for our system, since it is
tions [21]. Considering each unit cell as an element of the
planar array, the far field of the meta-surface can be ob- out of scope for this work. In reconfigurable meta-surface
generating different coding sequence for unit cells, we are
tained as:
able to achieve desired functionalities such as beam steer-
ing and radiated wave modulation. In this regard, the am-
( , Φ) = ( , Φ) ⋅ ( , Φ), (1) plitude Γ and phase Φ of the ( , )-th unit cell need

to be determined somehow which the entire response of
by considering infinite sphere, is the elevation angle, Φ the array matches with the required functionality. After
is the azimuth angle of an arbitrary direction in this coor- this step, by mapping the required Γ and Φ to the clos-
dination. est available unit cell states, the desired functionality will
be obtained. In the case of anomalous reflection for beam
Regarding the planar array, the pattern function of each steering, analytical methods provide high accuracy.
unit cell ( , Φ) is the element factor and the pattern

function of full planar configuration ( , Φ) is the array In this study, in order to obtain beam steering function-

factor. In far field region, we assume a planar wave covers ality, the phase gradient approach is used to determine
the entire meta-surface. Therefore, the radiated pattern the direction of reflection [13]. Considering Φ( , ) as the
will depend only on the array factor. In this case, the far phase profile which is imposed by reconfigurable meta-
̂
field pattern for the meta-surface with × unit cells, surface, the virtual wave vector K Φ = Φ x + Φ ̂y can be

© International Telecommunication Union, 2020 81